Answer :
Answer:
[tex]\frac{dy}{dt} = 102[/tex]
Step-by-step explanation:
step(i)
Given function y = 3 x³ - 2 x ... (i)
Differentiating equation (i) with respective to 'x'
[tex]\frac{dy}{dx} = 3 (3 x^{2} ) - 2(1)[/tex]
Given x = -2
[tex](\frac{dy}{dx} ) x_{=-2} = 3 (3 (-2)^{2} ) - 2(1)[/tex]
[tex](\frac{dy}{dx} ) x_{=-2} = 36 -2 =34[/tex]
Step(ii):-
we know that
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Given [tex]\frac{dx}{dt} = 3 and \frac{dy}{dx} = 34[/tex]
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
substitute values [tex]\frac{dx}{dt} = 3 and \frac{dy}{dx} = 34[/tex]
⇒ [tex]34 = \frac{\frac{dy}{dt} }{3 }[/tex]
cross multiplication , we get
[tex]\frac{dy}{dt} = 34( 3 ) = 102[/tex]
Final answer:-
[tex]\frac{dy}{dt} = 34( 3 ) = 102[/tex]